Method of variations of potential of quasi-periodic Schrodinger equation
classification
🧮 math-ph
math.MP
keywords
potentialequationquasi-periodicschrodingertypicalvariationsconstantcoupling
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We study the one-dimensional discrete quasi-periodic Schrodinger equation. We introduce the notion of variations of potential and use it to define "typical" potential. We show that for typical C^3 potential, if the coupling constant is large, then for most frequencies, the Lyapunov exponent is positive for all energies.
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